Download Multistage Cross-Sell Model of Employers in the Financial Industry

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Data Mining Techniques
Paper 124-28
Multistage Cross-Sell Model of Employers in the Financial Industry
Kwan Park and Steve Donohue
The Principal Financial Group
SEMMA methodology was applied.
Strong non-linear
relationships among the input variables were found and these
non-linear curvatures contributed to the models in different ways.
ABSTRACT
This paper details the steps to develop a multistage cross-sell
model of employers in the Financial Services industry. This
model can be used to score the likelihood of an employer to
purchase multiple products.
Topics covered include data
preparation for data mining, several advanced modeling
techniques, and multistage cross-sell model score comparison.
Strong non-linear curvatures among the input variables were
found during the modeling process and examined. The modeling
techniques used were Decision Tree, Neural Network, Regression
and Memory Based Reasoning in SAS Enterprise Miner (version
4.1) of Windows 2000 system.
OBJECTIVE
The objectives for this modeling are the following:
1. Identify employers with a high likelihood of becoming multiple
product owners.
2. Determine the product purchase sequence.
3. Assign a score according to likelihood to purchase identified
product.
DATA
This study deals with two types of data for each of the three
employer groups:
INTRODUCTION
In the Financial Services industry, the cross-selling and retaining
of customers have become very important issues. These issues
have been addressed via the development of many predictive
models. These models have been designed to identify customers
having a high likelihood of purchasing multiple products.
However, the vast majority of these models have been done at
the business-to-consumer level. The independent variables for
these models have generally included transactional data:
transaction frequency, amount of transaction and purchase
sequence, and demographic data (age, gender, income,
geographic location, etc.)
Transactional data – product coverage, length of relationship,
total contract amount, premium amount, number of active
employees under contract, etc.
Firmagraphic data – geographic region, metropolitan area, total
number of employees, sales volume, years in business, number
of customers, legal status, gender of CEO, private/public
company, SIC industry code, etc.
(The firmagraphic data was extracted from Dun and Bradstreet
and matched with tax-id.)
MODELING
The first object function of the modeling efforts was to predict the
multiple product employers.
Alternatively, this paper explains an approach for multistage
cross-sell modeling at the business-to-business (or employer)
level. For example, it examines selling Group Medical Insurance
to employers Group Long-Term Disability plans. The independent
variables used were employer level transactional data (years of
relationship, number of products owned, total premium values,
and firmagraphic data (total number of employees, residential
population, sales volume, standard SIC code, legal status, region,
etc.) The object of the modeling being to score the employers on
likelihood to become multiple products owners and predict the
sequence of product purchase.
1. Data was sampled to insure the same size of the prior target,
and partitioned as training and validation data set of 60% and
40%, respectively, with strata information of prior target
probability.
2. Data Mining Database Node was used to produce only one
data mining database, which optimized the performance of
analytic nodes.
Three sets of products were analyzed:
Group Insurance,
Pension, and Executive Benefits. Included in Group Insurance
were Medical/Health, Dental, Vision, Long-Term Disability, ShortTerm Disability, and Life. Within the Pension set were 401(K)
plans and Defined benefit cases. As for Executive Benefits, 19
product lines were utilized. Dun and Bradstreet employer data
was employed for the firmagraphic data. SAS Enterprise Miner
was used for modeling and the modeling techniques were
decision trees, neural network, logistic regression and memory
based reasoning.
For the development procedure, SAS’s
3. Missing values were replaced by ‘tree imputation with
surrogates’ method. This method is identical to tree imputation,
with the addition of surrogate splitting rules. A surrogate rule is a
back up to the main splitting rule. When the main splitting rule
relies on an input whose value is missing, the first surrogate rule
is invoked. If the first surrogate also relies on an input whose
value is missing, the next surrogate is invoked. If missing values
prevent the main rule and all the surrogates from applying to an
observation, the main rule assigns the observation to the branch
assigned to receive missing values.
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4. Decision Tree, Neural Network, Logistic Regression and
Memory Based Reasoning technologies were applied to predict
the potential multiple products owners.
Among the Least Squares, Gini reduction and Entropy reduction,
Gini with Model assessment measure of ‘Total leaf impurity’
showed the best model.
The Gini index is interpreted as the probability that any two
elements of a multiset chosen at random with replacement are
different. A pure node has a Gini Index of 0, as the number of
evenly distributed classes increases, the Gini index approaches 1.
This network model is somewhat more complex than usual neural
network model architecture. The choice of model complexity is
always an issue to modelers. The above architecture was chosen
by trial and error among many possible architectures
The Gini Index formula is as follows:
r
1 − å p 2 j = 2å p j p k
j =1
This multiplayer perceptron (MLP) is a feed-forward neural
network that uses sigmoid activation functions. This MLP is one of
the most common types of neural network used for supervised
prediction.
Empirically, it is often found that the tangent
hyperbolic function give rise to faster convergence of training
algorithms than the logistic functions.
j<k
Entropy is another measure of variability of categorical data.
Consider
r
mutually
exclusive
events
p1 , p 2 ,L, p r , then Entropy is defines as:
with
probabilities
r
H ( p1 , p 2 , L , p r ) = − å pi log 2 ( pi )
Another alternative of the function is ordinary radial basis function
i =1
(ORBF). ORBF networks are universal approximators in theory,
but in practice they are often ineffective multivariate function
estimators. In this modeling, ORBF networks were excluded.
Chi-Squared test statistic is as follows:
χν2 = å
(O − E ) 2
E
The most common incorrect concept of a neural network is that it
cannot be explained or cannot be represented as an equation.
However, a neural network is an application of non-linear
regression that can be represented as a single equation even
though that equation is very complicated. The beauty of a neural
network is that it can find very complicated non-linear relationship
among variables under the condition that the errors are quite
small.
The artificial neural network was originally developed by
researchers who were trying to mimic the neural system of the
human brain. By combining many simple computing elements
into a highly interconnected system, these researchers hoped to
produce complex phenomena such as intelligence. While there is
considerable controversy over whether artificial neural networks
are really intelligent, there is no doubt that they have developed
into very useful statistical models. More specifically, feedforward
neural networks are a class of flexible nonlinear regression,
discriminant, and data reduction models. By detecting complex
nonlinear relationships in data, neural networks can help to make
predictions about real-world problems.
As the target variable is a dichotomous variable, a logistic
regression model was used, and for the memory based reasoning
model, a default setup was used. Usually, many modelers favor
the backward selection method because it evaluates all the input
variables in relation to the target variable. In this modeling
process, stepwise selection, backward selection and forward
selection methods were applied to develop regression model, and
stepwise method showed the best performance. The logistic
regression equation is as follows:
Neural Network architecture was set as one layer of five hidden
nodes, and ordinal, nominal and interval variables and hidden
nodes were used an inputs to target variable. Hyperbolic Tangent
function was used as activation function and general linear
combination function was used. The tangent hyperbolic function
is defined as
g (a ) =
ö÷ = β + x β + x β + L x β
log æç p
0
1 1
2 2
n n
è 1− pø
ea − e−a
ea + e−a
The last modeling technique applied in this modeling is memorybased reasoning (or case based reasoning). It is a process that
identifies similar cases from history data or a database and
applies the information that is obtained from these cases to a new
The network architecture was:
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proc sql;
create table scored as
select a._node_ , a.single, b.multiple
from (select _node_, count(dunsno) as single
from &_score
where multiple='Single'
group by _node_ ) a
left join
(select _node_ , count(dunsno) as multiple
from &_score
where multiple='Multiple'
group by _node_ ) b
on a._node_ = b._node_ ;
quit;
record. The memory based reasoning node in SAS Enterprise
Miner is a modeling tool that uses a k-nearest neighbor algorithm
to categorize or predict observations. The k-nearest neighbor
algorithm takes a data set and a probe, where each observation
in the data set is composed of a set of variables and the probe
has one value for each variable. The distance between an
observation and the probe is calculated. The k observations that
have the smallest distances to the probe are the k-nearest
neighbor to that probe. A default set up of memory based
reasoning node was used in this modeling.
5. The decision tree showed the highest lift values within the top
30 percentiles. It produced nine segmentations and the following
proc sql (statement is to compute the lift values of each nodes.)
data scored;
set scored;
if multiple=. then multiple=0;
total=single+multiple;
score=int(multiple/total*10000)/100;
run;
Enterprise Miner Diagram
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6. Node Description
The following table explains the node definitions and lift values
Segment
Lift
Years of Business >100 years AND
Public/Private IS NOT MISSING AND
Sales Volume IS : [0] [1M,2M] [100M,500M]
1.99
Headquarter Location AND
Sales Volume IS : [2M,100M]
1.62
Single Location AND
1.49
Sales Volume IS : [2M,100M]
Years of Business IS : (5,100] AND
Public/Private IS NOT MISSING AND
Sales Volume IS : [0] [1M,2M] [100M,500M]
1.15
Years of Business IS : (0,5] AND
Public/Private IS NOT MISSING AND
Sales Volume IS : [0] [1M,2M] [100M,500M]
0.95
Sales Volume IS: [300K,400K] [500K,1M] [500M+]
0.56
Sales Volume IS : [1,300K] [400K,500K]
0.36
Location Status IS MISSING AND
Sales Volume IS : [2M,100M]
0.00
Public/Private IS MISSING AND
Sales Volume IS : [0] [1M,2M] [100M,500M]
0.00
to run the association node. The next table is the top 15 product
sequences.
Product A à Product B showed the highest
frequency of product purchasing sequence followed by Product B
à Product A.
The lift values of the top four nodes are greater than 1, and the
employers in these four nodes were selected to find the sequence
of the next products. For this analysis SAS Enterprise Miner’s
Association node was applied.
This is the second objective
function of this modeling. The product purchase date is needed
Product Sequence
Frequency
Percent
Product A ==> Product B
1,109
5.71
Product B ==> Product A
874
2.13
Product A ==> Product C
531
2.73
Product C ==> Product A
422
1.84
Product A ==> Product D
343
1.77
Product A ==> Product E
313
1.61
Product B & Product C ==> Product A
280
1.89
Product A ==> Product F
279
1.44
Product A ==> Product B & Product C
279
1.44
Product F ==> Product A
244
1.21
Product A ==> Product B & Product E
243
1.25
Product A ==> Product B & Product D
243
1.25
Product E ==> Product A
240
2.77
Product D ==> Product A
238
3.68
Product B ==> Product C
234
0.57
only the top six nodes were chosen. Each was then scored for
each individual employer.
Next, the cross-sell scores were
computed. The following table is an example of the scores.
7. The second stage models are to predict the employers who will
be Product B among current Product A customers and to predict
the employers who will be Product B customers among current
Product A customers, etc. Since so many models are required,
.
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Employer ID
Cross sell
score
Product A
è
Product B
Product B
è
Product A
Product A
è
Product C
Product C
è
Product A
Product A
è
Product D
Product A
è
Product E
3201767
8.72
6.79
0.00
0.23
0.00
5.26
5.10
1905289
8.72
3.25
0.00
0.62
0.00
7.98
6.65
6706752
8.72
0.00
4.85
0.15
6.23
0.62
1.52
1008754
7.13
1.65
4.85
0.23
3.50
5.26
1.52
2709015
7.13
2.76
3.21
4.52
0.00
3.31
1.52
Etc.
Steve Donohue
The Principal Financial Group
711 High Street
Des Moines IA, 50392
Work Phone: (515)362-2860
Fax: (515)283-5332
Email: [email protected]
Web: www.principal.com
APPLICATION
The application of this approach is to aid the cross-sell marketing
efforts at the employer level. Employers can be selected and
appropriately targeted based on their propensity to purchase
selected products. Marketing campaigns can be designed to
focus on those employers that are most likely to purchase. Thus,
this methodology can greatly impact the efficiency of marketing
campaigns.
SAS and all other SAS Institute Inc. product or service names are
registered trademarks or trademarks of SAS Institute Inc. in the
USA and other countries. ® indicates USA registration. Other
brand and product names are trademarks of their respective
companies.
CONCLUSION
This paper describes employer level cross sell modeling to
identify the likelihood of purchasing multiple products and the
product purchase sequence. It should also be noted that
campaign results of employer level cross sell can take more effort
and time compared to employee level campaign. Tracking must
be established to identify the impact of any marketing efforts.
REFERENCES
Bishop, C.M. (1995), Neural Networks for Pattern Recognition,
New York: Oxford University Press.
Breiman, L., Friedman, J. H., Olshen, R.A., and Stone, C. J.
(1984), Classification and Regression Trees, Chapman and Hall.
Enterprise Miner Software, Online Tutorial (SAS V8).
Ripley, B.D. (1996), Pattern Recognition and Neural Networks,
Cambridge University Press.
Rud, Olivia Parr (2001), Data Mining Cookbook, New York:
John Wiley & Sons.
Zahavi, J. and Levin, N. (1997), “Applying Neural Computing to
Target Marketing,” Journal of Direct Marketing, 11, 5-22.
CONTACT INFORMATION
Your comments and questions are valued and encouraged.
Contact the author at:
Kwan Park
The Principal Financial Group
711 High Street
Des Moines IA, 50392
Work Phone: (515)247-5647
Fax: (515)283-5332
Email: [email protected]
Web: www.principal.com
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